Related papers: Projecting onto a Capped Rotated Second-Order Cone
Projections onto sets are used in a wide variety of methods in optimization theory but not every method that uses projections really belongs to the class of projection methods as we mean it here. Here projection methods are iterative…
New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each…
We study intersections of projective convex sets in the sense of Steinitz. In a projective space, an intersection of a nonempty family of convex sets splits into multiple connected components each of which is a convex set. Hence, such an…
Let $C$ be a closed convex subset of a real Hilbert space containing the origin, and assume that $K$ is the homogenization cone of $C$, i.e., the smallest closed convex cone containing $C \times \{1\}$. Homogenization cones play an…
This monograph is on convex real projective structures on strongly tame n-orbifolds with some appropriate conditions on ends.
In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…
We fully characterize orthogonal projections of infinite right circular (round) cones in real Hilbert spaces. Another interpretation is that, given two vectors in a real Hilbert space, we establish the optimal estimate on the angle between…
We define two non-linear operations with random (not necessarily closed) sets in Banach space: the conditional core and the conditional convex hull. While the first is sublinear, the second one is superlinear (in the reverse set inclusion…
In this paper, we study the iteration complexity of cubic regularization of Newton method for solving composite minimization problems with uniformly convex objective. We introduce the notion of second-order condition number of a certain…
This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support…
The method of alternating projections involves orthogonally projecting an element of a Hilbert space onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm if the projections are taken…
For a given polyhedral convex set-valued mapping we define a polyhedral convex cone which we call the natural ordering cone. We show that the solution behavior of a polyhedral convex set optimization problem can be characterized by this…
For every finite closure space $X$ one can define a finite topological space $\operatorname{Top} X$ together with a natural projection $\operatorname{Top} X\longrightarrow X$. This could allow to apply the techniques of topological…
Two approximation algorithms for solving convex vector optimization problems (CVOPs) are provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously. The first algorithm is an extension of Benson's outer…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
This paper explores a natural generalization of Euclidean projection through the lens of strongly quasiconvex functions, as developed in prior works. By establishing a connection between strongly quasiconvex functions and the theory of…
We prove that the Douglas--Rachford method applied to two closed convex cones in the Euclidean plane converges in finitely many steps if and only if the set of fixed points of the Douglas--Rachford operator is nontrivial. We analyze this…
The projector onto the Minkowski sum of closed convex sets is generally not equal to the sum of individual projectors. In this work, we provide a complete answer to the question of characterizing the instances where such an equality holds.…
Relaxation and rounding approaches became a standard and extremely versatile tool for constrained submodular function maximization. One of the most common rounding techniques in this context are contention resolution schemes. Such schemes…
We introduce holed cone structures on 3-manifolds to generalize cone structures. In the same way as a cone structure, a holed cone structure induces the holonomy representation. We consider the deformation space consisting of the holed cone…